Session Hj - Shocks, Combustion & Hypersonic Flows.
ORAL session, Tuesday, November 25
310, Moscone Center
In kinetic theory of gases the Chapman-Enskog (CE) expansion gives an expression for the first order nonequilibrium fluxes in terms of variables conjugate to the conserved variables. For classical monatomic gases these conjugate variables can be simply expressed in terms of the conserved hydrodynamic densities. In contrast, this relationship is not simple for a discrete-velocity gas, i.e., the Navier-Stokes (NS) equation for a discrete-velocity gas is generally not a simple system for \rho, \rho\u, and \rho (e+u^2/2). In such a case, the direct use of conjugate variables is natural. In this talk, we present the CE expansion for a nine-velocity gas with the above choice of variables in the context of a 1D shock wave, and compare the resulting NS shock profile to the full Boltzmann profile. The conjugate variables and the discrete-velocity gas also prove to be useful tools in evaluating various high-order moment closures proposed for the transitional regimes.